Related papers: Zero-Energy Fields on Complex Projective Space
Using complexified quaternions, a formalism without Lorentz frames, and therefore also without vierbeins, for dealing with tensor and spinor fields in curved spacetime is presented. A local U(1) gauge symmetry, which, it is speculated,…
In this paper we construct and study a formulation of a chargeless complex vector matter field in a supersymmetric framework. To this aim we combine two no-chiral scalar superfields in order to take the vector component field to build the…
In this paper, we study a kernel smoothing approach for denoising a tensor field. Particularly, both simulation studies and theoretical analysis are conducted to understand the effects of the noise structure and the structure of the tensor…
We analyse in detail the quantization of a simple noncommutative model of spontaneous symmetry breaking in zero dimensions taking into account the noncommutative setting seriously. The connection to the counting argument of Feyman diagrams…
The effective potential of composite fermion fields in three-dimensional Thirring model in curved spacetime is calculated in linear curvature approximation. The phase transition accompanied by the creation of non-zero chiral invariant…
The cosine transforms of functions on the unit sphere play an important role in convex geometry, the Banach space theory, stochastic geometry and other areas. Their higher-rank generalization to Grassmann manifolds represents an interesting…
We consider the Krein realization of the Hilbert space for a massless scalar field in 1+1 dimensions. We find convergence criteria and the completion of the space of test functions ${\cal S}$ with the topology induced by the Krein scalar…
A central objective in inverse problems arising in integral geometry is to understand the kernel characterization, inversion formulas, stability estimates, range characterization, and unique continuation properties of integral transforms.…
Based on direct integrals, a framework allowing to integrate a parametrised family of reproducing kernels with respect to some measure on the parameter space is developed. By pointwise integration, one obtains again a reproducing kernel…
The approach of metric-affine field theory is to define spacetime as a real oriented 4-manifold equipped with a metric and an affine connection. The 10 independent components of the metric tensor and the 64 connection coefficients are the…
Given a degeneration of compact projective complex manifolds $X$ over the punctured disc, with meromorphic singularities, and a relatively ample line bundle $L$ on $X$, we study spaces of plurisubharmonic metrics on $L$, with particular…
A four-index tensor is constructed with terms both quadratic in the Riemann tensor and linear in its second derivatives, which has zero divergence for space-times with vanishing scalar curvature. This tensor reduces in vacuum to the…
By way of concrete presentations, we construct two infinite-dimensional transforms at the crossroads of Gaussian fields and reproducing kernel Hilbert spaces (RKHS), thus leading to a new infinite-dimensional Fourier transform in a general…
We study metric transformations including not just the field strength tensor of a $U(1)$ gauge field, but also its dual tensor. We first consider an arbitrary symmetric matrix built up with these two tensors in the metric transformation. It…
The geometry of antisymmetric fields with nontrivial transitions over a base manifold is described in terms of exact sequences of cohomology groups. This formulation leads naturally to the appearance of nontrivial topological charges…
Consider a compact Riemannian manifold of dimension $\geq 3$ with strictly convex boundary, such that the manifold admits a strictly convex function. We show that the attenuated ray transform in the presence of an arbitrary connection and…
Transient X-ray absorption techniques can measure ultrafast dynamics of the elemental edges in a material or multiple layer junction, giving them immense potential for deconvoluting concurrent processes. However, the interpretation of the…
Focus of this study is to explore some aspects of mathematical foundations for using complex manifolds as a model for space-time. More specifically, certain equations of motions have been derived as a Projective geodesic on a real manifold…
We give a `geometrical' construction of an action of a Heisenberg algebra on the homology of the moduli spaces of torsion free sheaves on a complex smooth connected projective surface, framed along a smooth connected genus zero curve. This…
We give a simplified account of the properties of the transfer matrix for a complex one-dimensional potential, paying special attention to the particular instance of unidirectional invisibility. In appropriate variables, invisible…